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asin(x/sqrt(x^2+1))
Derivada de la función/ x^2+1/ asin(x/sqrt(x^2+1))

Derivada de asin(x/sqrt(x^2+1))

Función f() - derivada -er orden en el punto
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
    /     x     \
asin|-----------|
    |   ________|
    |  /  2     |
    \\/  x  + 1 /
asin⁡(xx2+1)\operatorname{asin}{\left(\frac{x}{\sqrt{x^{2} + 1}} \right)} 
asin(x/sqrt(x^2 + 1))
Gráfica
02468-8-6-4-2-10105-5
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                    2    
     1             x     
----------- - -----------
   ________           3/2
  /  2        / 2    \   
\/  x  + 1    \x  + 1/   
-------------------------
          ____________   
         /        2      
        /        x       
       /   1 - ------    
      /         2        
    \/         x  + 1
−x2(x2+1)32+1x2+1−x2x2+1+1\frac{- \frac{x^{2}}{\left(x^{2} + 1\right)^{\frac{3}{2}}} + \frac{1}{\sqrt{x^{2} + 1}}}{\sqrt{- \frac{x^{2}}{x^{2} + 1} + 1}}
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Segunda derivada [src] 
  /                                       2\
  |                          /        2  \ |
  |                          |       x   | |
  |          ____________    |-1 + ------| |
  |         /        2       |          2| |
  |        /        x        \     1 + x / |
x*|- 3*   /   1 - ------  + ---------------|
  |      /             2                3/2|
  |    \/         1 + x     /       2  \   |
  |                         |      x   |   |
  |                         |1 - ------|   |
  |                         |         2|   |
  \                         \    1 + x /   /
--------------------------------------------
                        3/2                 
                /     2\                    
                \1 + x /
x(−3−x2x2+1+1+(x2x2+1−1)2(−x2x2+1+1)32)(x2+1)32\frac{x \left(- 3 \sqrt{- \frac{x^{2}}{x^{2} + 1} + 1} + \frac{\left(\frac{x^{2}}{x^{2} + 1} - 1\right)^{2}}{\left(- \frac{x^{2}}{x^{2} + 1} + 1\right)^{\frac{3}{2}}}\right)}{\left(x^{2} + 1\right)^{\frac{3}{2}}}
Simplificar
Tercera derivada [src] 
                          /        2  \ /        2          4  \                                           3  
                          |       x   | |     5*x        4*x   |        /        2  \         /        2  \   
                          |-1 + ------|*|1 - ------ + ---------|      2 |       x   |       2 |       x   |   
                          |          2| |         2           2|   6*x *|-1 + ------|    3*x *|-1 + ------|   
           4         2    \     1 + x / |    1 + x    /     2\ |        |          2|         |          2|   
       15*x      18*x                   \             \1 + x / /        \     1 + x /         \     1 + x /   
-3 - --------- + ------ - -------------------------------------- + ------------------ - ----------------------
             2        2                        2                              2                              2
     /     2\    1 + x                        x                          1 + x                   /       2  \ 
     \1 + x /                           1 - ------                                      /     2\ |      x   | 
                                                 2                                      \1 + x /*|1 - ------| 
                                            1 + x                                                |         2| 
                                                                                                 \    1 + x / 
--------------------------------------------------------------------------------------------------------------
                                                          ____________                                        
                                                3/2      /        2                                           
                                        /     2\        /        x                                            
                                        \1 + x /   *   /   1 - ------                                         
                                                      /             2                                         
                                                    \/         1 + x
−15x4(x2+1)2+6x2(x2x2+1−1)x2+1+18x2x2+1−3x2(x2x2+1−1)3(x2+1)(−x2x2+1+1)2−3−(x2x2+1−1)(4x4(x2+1)2−5x2x2+1+1)−x2x2+1+1(x2+1)32−x2x2+1+1\frac{- \frac{15 x^{4}}{\left(x^{2} + 1\right)^{2}} + \frac{6 x^{2} \left(\frac{x^{2}}{x^{2} + 1} - 1\right)}{x^{2} + 1} + \frac{18 x^{2}}{x^{2} + 1} - \frac{3 x^{2} \left(\frac{x^{2}}{x^{2} + 1} - 1\right)^{3}}{\left(x^{2} + 1\right) \left(- \frac{x^{2}}{x^{2} + 1} + 1\right)^{2}} - 3 - \frac{\left(\frac{x^{2}}{x^{2} + 1} - 1\right) \left(\frac{4 x^{4}}{\left(x^{2} + 1\right)^{2}} - \frac{5 x^{2}}{x^{2} + 1} + 1\right)}{- \frac{x^{2}}{x^{2} + 1} + 1}}{\left(x^{2} + 1\right)^{\frac{3}{2}} \sqrt{- \frac{x^{2}}{x^{2} + 1} + 1}}
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Gráfico
Derivada de asin(x/sqrt(x^2+1))
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